Multiscale modeling of optical and transport properties of solids - PowerPoint PPT Presentation

Multiscale modeling of optical and transport properties of solids and nanostructures Yia-Chung Chang Research Center for Applied Sciences (RCAS) Academia Sinica, Taiwan NTU Colloquium , March 14, 2017 In collaboration with Ming-Ting Kuo, NCU S. J. Sun, J. Velev, Gefei Qian, Hye-Jung Kim, UIUC Zhenhua Ning, Chih-Chieh Chen, UIUC/RCAS Ching-Tang Liang, I-Lin Ho, RCAS J. W. Davenport, R. B. James, BNL T. O. Cheche, U. Burcharest, W. E. Mahmoud

Outline • Optical excitations of solids/nanostructures modeled by: density-functional theory (DFT), tight-binding (TB), k.p model, and effective bond-orbital model (EBOM) • Transport and thermoelectric properties of nanostructure junctions modeled by non-equilibrium Green function method, including correlation • Examples: zincblende/cubic semiconductors, quantum wires, and QDs and QD tunnel junctions

Excitation spectra Flow chart of BSE calculation for excitation spectra [ G. Onida, L. Reining, A. Rubio Rev. Mod. Phys., 74, 601, (2002)] DFT packages: VASP, CASTEP Abinit WIEN2K LMTO SIESTA LASTO

Linearized Slater-type orbital (LASTO) method [J. W. Davenport, Phys. Rev. B 29, 2896 (1994)] • Inside MTs: exact numerical solution (u) & du/dE • Outside MTs: Slater-type orbitals, r n-1 e -br Y lm ( Ω ) • Match boundary conditions for each spherical harmonics

Symmetry-adapted basis [Y.-C. Chang, R. B. James, and J. W. Davenport, PRB 73 , 035211 (2006)] Use of symmetry can reduce the computation effort significantly • Symmetry-adapted basis was not 128-atom fcc supercell commonly adopted in DFT calculations • (For general k, point symmetry is lost) • For large supercell calculations, only k=0 is needed, the use of symmetry- adated basis can be very beneficial • Examples: 1. Defects in solids with high point symmetry 2. High-symmetry nanoparticles like C60. 3. Optical excitations of nanoclusters • Irreducible 4. Excitonic excitation of solids with high symmetry segment

Optically allowed transitions for T d group • Only the following 6 (& exch.) out of 100 possible configurations are allowed: • Polarization matrix in RPA: [Use FFT] • Polarization matrix in symmetry-adapted basis: Using Wigner-Ekart theorem:

Optical spectra calculated by Bathe-Salpeter Eq. in LASTO basis Si LiF • BSE (solid line) • RPA (dashed line) • Results similar to LAPW results: • [Puschnig* and C. Ambrosch-Draxl, PRB 66 , 165105 (2002)]

Optical spectra of GaAs, AlAs & SLs GaAs AlAs AlAs 1X1 SL GaAs Exp [Exp. data taken from [M. Garriga et al., Phys. Rev. B 36 , 3254 (1987)]

Supercell method in plane-wave basis

• Symmetrized Plane-wave basis •Ψ = Σ s C(G s )|G s > • The star of G • (001) • G • G s s • (010) • (001) • dzt • 10

• dzt • 11

• dzt • 12

The meta-Generalized Gradient Approximation mGGA (TB09) [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)] Becke-Roussel exchange potential [A.D. Becke & M.R. Roussel, Phys. Rev. A 39, 3761 (1989)] TDDFT with mGGA : [V.U. Nazarov & G. Vignale, PRL 107, 216402(2011)]

Band structure comparison

Comparison between LASTO & WIEN2k

Excitation spectra Si GaAs

Dielectric functions of InGaAs & InAsP alloys obtained by TDDFT based on mGGA [F. Tran and P. Blaha, PRL 102, 226401 (2009)] [V.U. Nazarov and G. Vignale, PRL 107 , 216402(2011)]

Bond-orbital model [S. Sun,Y. C. Chang, PRB 62, 13631 (2000)]       H k E ' '     , p ,                   2    2  1 ik e E E E E    ' '    xy xx xy zz ,  Strain H am iltonian      V D 3 de 3 de   H 1 xy xz       H 3 de V D 3 de st xy H 2 yz      3 de 3 de V D   2 xz yz H 3 3 e ij =(  ij +  ji )/2  V H =(a 1 +a 2 )(  xx +  yy +  zz ) i D 1 =b(2  xx -  yy -  zz ) D 2 =b(2  yy -  xx -  zz ) D 3 =b(2  zz -  xx -  yy ) 4 a 1 , a 2 , b, d = deform ation potentials. 1

InAs/GaAs Self assembled quantum dots Incident light InAs Wetting layer Area density GaAs 11 / Infrared detector 2 10 cm Lattice mismatch 7% Laser

Bond-orbital model [S. Sun,Y. C. Chang, PRB 62, 13631 (2000)] s v’ s v y (0,1,0) x (0,0,1)

Valence force field (VFF) Model   1 3  2   2  2 2 V d d d 0 , 0 , 4 4 ij ij ij ij ij     1 3   2     3 d d d d d d 0 , 0 , 0 , 0 , 2 4 4 ijk ij ik ij ik ij ik  i j k 3 i labels atom positions d i2 d i3 j , k label nearest-neighbors of i d ij = bond length joining sites i and j i d 0,ij is the corresponding equilibrium length d i4  ij = bond stretching constants d i1 d ijk = bond bending constants 4 We take d ijk 2 = d ij d ik 1

Ground Transition Energy Varying With Dot Height (comparing to Experiment) UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Dot base length 200Å 1.24 Theory Theoty 1.20 Energy (eV) Experiment 1.16 1.12 1.08 1.04 20 40 60 80 100 Island height (A)

PL/PLE Characterization: Electronic Structure InAs WL InAs/GaAs QDs PL Intensity (arb. units) 3ML PIG GaAs GaAs T=7K QD I EXC ~5000W/cm 2 E EXC =2.41eV ~310+50meV Log of Intensity (arb. units) E c strongest transitions PLE E WL e E DET =1.062eV E 3 50meV E weaker transitions 2 59meV E 1 +LO phonon transition V V e e 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 2 5 5 4 1.062eV 1.229eV 1.121eV 1.197eV 1.147eV Energy (eV) . . 1 1 ? Ground state at 1.062eV Excited states: H 1,2 26meV Strongest at 1.147eV and 1.229eV H 32meV 3 H E WL Weaker at 1.121eV and 1.197eV 4 h E v ~150+50meV [Data from A. Madhkar (USC)]

Intra-band Transitions 0.4 ~310+50meV ~310+50meV Normal incidence 162 meV WL E E c E c e 7.62 m m Bias: -0.5 V WL E Photocurrent (nA) e 0.3 @77K E 3 50meV E 5 184 meV E E 4 59meV 2 6.7 m m 0.2 E 1 E 3 V e E 5 2 4 V V V V V . 0.1 1 e e e e e 110 meV E 1 1 7 2 7 9 2 9 6 4 2 V V V 11.3 m m 2 1 1 0 1 e e e . . . . . 1 1 1 1 1 m m m 2 0 4 H 1,2 6 26meV 1 8 0.0 1 1 1 H 32meV 3 2500 2000 1500 1000 H 4 -1 ) Wavenumber (cm E v E WL ~150+50meV h Data from A. Madhkar (USC)

Intra-band Transitions Table 4 Inter-sub band transition matrix elements of ground electron state to upper  2 three electron states, . B=200A, h=80A.   r 1 , c i c , Symmetry state i x y z (Ei(DEE1E1)E 0.2 A1 #2 (0.111) 0 0 0 0 #3 (0.123) 57 #4 (0.197) 0 0 201 28.5 A2 #2 (0.106) 0 0 0 0 #3 (0.114) 0 15 B1,B2 #2 (0.109) 0 0 0 0 #3 (0.138) 42 #4 (0.201) 0 0 14 0 A1-B1n #1 (0.062) 446 446 0.2 0.2 #2 (0.162) 0 #3 (0.218) 0.4 0.4 0 #2(0.049) 536 536 0 B1-A1n #3(0.061) 659 659 0 #4(0.135) 376 376 0 #5(0.161) 10.2 10.2 0

Effective bond-orbital model for QWRs [Y. C. Chang, W. E. Mahmoud, Comp. Phys. Comm., 196, 92 (2015)] • ( 4 4 4 4 4 4 • ( 2 2 2 2 2 2 b) a) InAs GaSb 0 0 0 0 0 0 E (eV) E (eV) -2 -2 -2 -2 -2 -2 -4 -4 -4 -4 -4 -4 -6 -6 -6 -6 -6 -6 -8 -8 -8 -8 -8 -8 -1 -1 -1 0 0 0 1 1 1 2 2 2 -1 -1 -1 0 0 0 1 1 1 2 2 2     L X K L X K Wave Vector, k Wave Vector, k 4 4 4 4 4 4 • ( • ( 2 2 2 2 2 2 c) d) GaAs CdTe 0 0 0 0 0 0 E (eV) E (eV) -2 -2 -2 -2 -2 -2 -4 -4 -4 -4 -4 -4 -6 -6 -6 -6 -6 -6 -8 -8 -8 -8 -8 -8 -1 -1 -1 0 0 0 1 1 1 2 2 2 -1 -1 -1 0 0 0 1 1 1 2 2 2     L X K L X K Wave Vector, k Wave Vector, k

2.0 2.0 2.0 0.0 0.0 0.0 • ( • ( InAs NW VB 1.8 1.8 1.8 a) b) d = 5nm -0.2 -0.2 -0.2 1.6 1.6 1.6 E (eV) E (eV) 1.4 1.4 1.4 -0.4 -0.4 -0.4 1.2 1.2 1.2 1.0 1.0 1.0 -0.6 -0.6 -0.6 InAs NW CB d = 5nm 0.8 0.8 0.8 -0.8 -0.8 -0.8 0.6 0.6 0.6 0.0 0.0 0.0 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5 1.5 2.0 2.0 2.0 2.5 2.5 2.5 0.0 0.0 0.0 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5 1.5 2.0 2.0 2.0 2.5 2.5 2.5 -1 -1 Wave Vector, k (nm ) Wave Vector, k (nm ) • ( • ( 2.0 2.0 2.0 0.0 0.0 0.0 InAs NW VB c) d) 1.8 1.8 1.8 d = 7nm -0.1 -0.1 -0.1 1.6 1.6 1.6 -0.2 -0.2 -0.2 E (eV) E (eV) 1.4 1.4 1.4 1.2 1.2 1.2 -0.3 -0.3 -0.3 1.0 1.0 1.0 InAs NW CB -0.4 -0.4 -0.4 d = 7nm 0.8 0.8 0.8 0.6 0.6 0.6 -0.5 -0.5 -0.5 0.0 0.0 0.0 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5 1.5 2.0 2.0 2.0 2.5 2.5 2.5 0.0 0.0 0.0 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5 1.5 2.0 2.0 2.0 2.5 2.5 2.5 -1 -1 Wave Vector, k (nm ) Wave Vector, k (nm )